I normally try to avoid posts on politics, especially Labour politics, since my views lost in the Labour leadership election then in the referendum about Europe. I am clearly on the wrong side, the others won so shut up.

However, you knew that would be coming didn’t you? The headline has given away that I am going to write something about the Leader of the Labour Party, that I did not support last year.

OK, so what great political insight have I come up with that requires a breaking of my self-ordained silence on the matter? Nothing. This is not a political post but a logical one. If you ask me to be more precise, a symbolic logic one. A search for how we can decide if a statement is true or not.

Symbolic logic tries, this is my own description from what I understood studying it so I know I may be wildly off course, to represent the logic of sentences with symbols so it is easier to understand the logical meaning and consequences of what we say, are they true or not.

The beginning of my study was “and statements” and “or statements.” Sentences with and in and/or ones with or in. How do we decide if they are true?

Basically, for statements involving “and” both parts of the statement had to be true for the statement to be true. Whereas, statements involving “or”, only one half of the statement had to be true for the statement to to be true. Symbolically it works out like this, I thank Hotmath.com for the following table:

# Symbolic Logic

## Conjunction (AND statements)

A conjunction is a compound statement formed by combining two statements using the word *and*. In symbolic logic, the conjunction of p and q is written p∧q.

A conjunction is true only if both the statements in it are true. The following truth table gives the truth value of p∧ depending on the truth values of p and q .

**p q p∧q**

T T T

T F F

F T F

F F F

So, for example, if we say “He likes oranges and lemons.” Then, if he likes lemons and oranges it is true, but if he likes lemons but not oranges then any statement saying he likes oranges and lemons or vice versa, will not be true as he does not like both of them. If he does not like both of them then any statement saying he likes both of them will not be true either.

**Disjunction(OR statements)**

A disjunction is a compound statement formed by combining two statements using the word *or*. In symbolic logic, the disjunction of p or q is written p∨q.

A disjunction is true if either one or both of the statements in it is true. The following truth table gives the truth value of p∨qp∨q depending on the truth values of pp and qq.

**p q ∨q**

F F F

T F T

F T T

T T T

So, if the statement is “He likes oranges or lemons.” will be true so long as he likes both of them, oranges, or lemons, but not if he hates them both.

Thus, using symbolic logic we can see that Jeremy Corbyn’s statement “I am not going to betray the trust of those who voted for me – or the millions of supporters across the country who need Labour to represent them,” logically means, he could betray the trust of those who voted for him, or the supporters across the country who need Labour to represent them. It is an “Or statement” so he could be seeking to betray anyone.

However, if both statements are true the whole statement is true. But, if that was the case, why not use an “and statement” to make sure the logic is clear and doubly locked in? I can only assume that by not using an “and statement” and by choosing an “or statement” Jeremy, or the people who speak for him, unwittingly highlighted a truth about him, that he, and/or they, know that he will betray the trust of one of them. He cannot keep the faith with both.

Is it “those who voted for me” or “the millions of supporters who need Labour to represent them?” Who does he think his continued leadership betrays?

The headline is my answer to that question.

Tags: current affairs, Daily life, democracy, Labour, philosphy, politics, Symbolic Logic

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